Application of Šapkarev's method to boundary value problems for linear complex second-order ordinary differential equations (Q2724050)

The authors consider and solve the Neumann-Schwarz boundary value problem for the second-order linear complex differential equation NEWLINE\[NEWLINE D^{(2)}w + \alpha(z, \overline z) Dw + \beta(z, \overline z) w = \gamma(z,\overline z), \qquad Dw = (u_x'- v_y') + i (u_y'+ v_x') = 2 w_{\overline z}', NEWLINE\]NEWLINE where \(\alpha(z, \overline z)\), \(\beta(z, \overline z)\) and \(\gamma(z, \overline z)\) are given continuous functions. The solution is obtained by the method of \textit{I. Šapkarev} [Bull. Soc. Math. Phys. Serbie 15, 21-27 (1963; Zbl 0135.12701)]. The authors also consider and solve a boundary value problem of Carleman's type for the same type of differential equation.